Question: Simplify the following expression: $q = \dfrac{r + 1}{r - 5} - \dfrac{-6r - 7}{r - 5}$
Since the expressions have the same denominator we simply subtract the numerators: $q = \dfrac{r + 1 - (-6r - 7)}{r - 5}$ Distribute the negative sign: $q = \dfrac{r + 1 + 6r + 7}{r - 5}$ Combine like terms: $q = \dfrac{7r + 8}{r - 5}$